Quantum spin glasses are often considered testbeds for studying quantum optimization algorithms and as such have been the subject of various quantum advantage claims. Here we investigate the near adiabatic dynamics of biclique quantum spin glasses within the (discrete) truncated Wigner approximation (TWA). Benchmarks on small systems show that TWA recovers sample-to-sample fluctuations of the Edwards-Anderson order parameter, over a wide range of annealing times, with increasing fidelity when the system size increases. We extract critical exponents from the Binder cumulant in line with theoretical expectations, reproducing recent quantum experiments. The computational cost of the method is minimal and it can easily be applied to tens of thousands of qubits.
Quantum spin glasses are often considered testbeds for studying quantum optimization algorithms and as such have been the subject of various quantum advantage claims. Here we investigate the near adiabatic dynamics of biclique quantum spin glasses within the (discrete) truncated Wigner approximation (TWA). Benchmarks on small systems show that TWA recovers sample-to-sample fluctuations of the Edwards-Anderson order parameter, over a wide range of annealing times, with increasing fidelity when the system size increases. We extract critical exponents from the Binder cumulant in line with theoretical expectations, reproducing recent quantum experiments. The computational cost of the method is minimal and it can easily be applied to tens of thousands of qubits.
A phase-space method, suitable to study the many-body spin dynamics in generic spin lattice models is introduced, discussed, and tested. This technique, which we refer to as the dTWA, is based on the discrete sampling of the Wigner function instead of the continuous sampling in traditional Truncated Wigner Approximation (TWA) methods. The power of the method is demonstrated by comparisons with analytical and numerically exact calculations, which show a significant improvement compared to the TWA, e.g. by capturing revivals of spin-observables. The dTWA is demonstrated to not only correctly reproduce dynamics of one-particle observables but also two-point correlations and spin squeezing, a property relying on entanglement. This method thus opens the possibility to study the quantum dynamics in long-range spin models, accessible to recent state-of-the-art experiments, in regimes where other numerical techniques are inapplicable.
An accurate description of the nonequilibrium dynamics of systems with coupled spin and bosonic degrees of freedom remains theoretically challenging, especially for large system sizes and in higher than one dimension. Phase-space methods such as the truncated Wigner approximation (TWA) have the advantage of being easily scalable and applicable to arbitrary dimensions. In this work we adapt the TWA to generic spin-boson models by making use of recently developed algorithms for discrete phase spaces [J. Schachenmayer, A. Pikovski, and A. M. Rey, Phys. Rev. X 5, 011022 (2015)]. Furthermore we go beyond the standard TWA approximation by applying a scheme based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations to our coupled spin-boson model. This allows us, in principle, to study how systematically adding higher-order corrections improves the convergence of the method. To test various levels of approximation we study an exactly solvable spin-boson model, which is particularly relevant for trapped-ion arrays. Using TWA and its BBGKY extension we accurately reproduce the time evolution of a number of one- and two-point correlation functions in several dimensions and for an arbitrary number of bosonic modes.
Abstract Numerical techniques to efficiently model out-of-equilibrium dynamics in interacting quantum many-body systems are key for advancing our capability to harness and understand complex quantum matter. Here we propose a new numerical approach which we refer to as generalized discrete truncated Wigner approximation (GDTWA). It is based on a discrete semi-classical phase space sampling and allows to investigate quantum dynamics in lattice spin systems with arbitrary S ≥ 1/2. We show that the GDTWA can accurately simulate dynamics of large ensembles in arbitrary dimensions. We apply it for S > 1/2 spin-models with dipolar long-range interactions, a scenario arising in recent experiments with magnetic atoms. We show that the method can capture beyond mean-field effects, not only at short times, but it also can correctly reproduce long time quantum-thermalization dynamics. We benchmark the method with exact diagonalization in small systems, with perturbation theory for short times, and with analytical predictions made for models which feature quantum-thermalization at long times. We apply our method to study dynamics in large S > 1/2 spin-models and compute experimentally accessible observables such as Zeeman level populations, contrast of spin coherence, spin squeezing, and entanglement quantified by single-spin Renyi entropies. We reveal that large S systems can feature larger entanglement than corresponding S = 1/2 systems. Our analyses demonstrate that the GDTWA can be a powerful tool for modeling complex spin dynamics in regimes where other state-of-the art numerical methods fail.
We develop and utilize the SU(3) truncated Wigner approximation (TWA) in order to analyze far-from-equilibrium quantum dynamics of strongly interacting Bose gases in an optical lattice. Specifically, we explicitly represent the corresponding Bose-Hubbard model at an arbitrary filling factor with restricted local Hilbert spaces in terms of SU(3) matrices. Moreover, we introduce a discrete Wigner sampling technique for the SU(3) TWA and examine its performance as well as that of the SU(3) TWA with the Gaussian approximation for the continuous Wigner function. We directly compare outputs of these two approaches with exact computations regarding dynamics of the Bose-Hubbard model at unit filling with a small size and that of a fully connected spin-1 model with a large size. We show that both approaches can quantitatively capture quantum dynamics on a timescale of $\ensuremath{\hbar}/(Jz)$, where J and z denote the hopping energy and the coordination number. We apply the two kinds of SU(3) TWA to dynamical spreading of a two-point correlation function of the Bose-Hubbard model on a square lattice with a large system size, which has been measured in recent experiments. Noticeable deviations between the theories and experiments indicate that proper inclusion of effects of the spatial inhomogeneity, which is not straightforward in our formulation of the SU(3) TWA, may be necessary.
We present a semiclassical phase-space method to calculate thermal and ground states of large interacting spin systems. To this end, we extend the recently developed truncated Wigner approximation for spins (TWA) to the imaginary time, termed iTWA. The evolution of the canonical density matrix in imaginary time is mapped to a partial differential equation of its Wigner function. Truncation at the Fokker-Planck level leads to a set of stochastic differential equations, which can be efficiently simulated even for large systems. We show that for general Ising Hamiltonians the approximation becomes exact for large imaginary times subject only to sampling errors. Thus the iTWA is ideal to determine the ground state of spin glasses or to find solutions to quadratic unconstrained binary optimization problems (QUBO) on a controlled approximation level. We illustrate this for MaxCut on random, unweighted 3-regular graphs, encoded in an anti-ferromagnetic Ising Hamiltonian, for which finding the exact ground state and even approximations to it beyond a certain accuracy is know to be NP hard. Furthermore, in order to assess the quality of the method also for general spin models, we analyze the ground-state quantum phase transition of the transverse-field Ising model in one and two spatial dimensions, finding reasonably good agreement with the exact behavior.
We put forward a user-friendly framework of the truncated Wigner approximation (TWA) for dissipative quantum many-body systems. Our approach is computationally affordable and it features a straightforward implementation. The leverage of the method can be ultimately traced to an intimate connection between the TWA and the semiclassical limit of the quantum Langevin equation, which we unveil by resorting to a path-integral representation of the Lindbladian. Our approach allows us to explore dynamics from early to late times in a variety of models at the core of modern atomic, molecular, and optical research, including lasing, central-spin models, driven arrays of Rydbergs, and correlated emission in free space. Notably, our TWA approach outperforms the cumulant-expansion method in certain models and performs comparably well in others, all while offering significantly lower computational costs and a much simpler formulation of the dynamical equations. We therefore argue that TWA could, in the near future, become a primary tool for a fast and efficient first exploration of driven-dissipative many-body dynamics on consumer-grade computers.